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Geometry
Mr. Schopper
Chapter 5 - TEST
Name ____________________ section _____
Properties of Polygons
I. Beside each “property” below, write all of the quadrilaterals that have that property.
1. The diagonals are congruent : ______________________________________
2. The diagonals are perpendicular ____________________________________
3. The diagonals bisect each other : ______________________________________
4. The diagonals bisect opposite angles : _______________________________________
5. Only one diagonal bisects a pair of opposite angles : ____________________________
II. Fill in the blank with the proper word. Do not use the word “SQUARE”.
6. An equiangular quadrilateral is more commonly called a ____________________.
7. An equilateral quadrilateral is more commonly called a _____________________.
8. The vertex angles of a kite are ______________ by a diagonal.
9. In a trapezoid, the _________________ is parallel to the _______________.
10. The length of a midsegment between two sides in a triangle is _____________ of the
length of the remaining side.
III. In each of the following, give the best name for the quadrilateral pictured (based upon the markings)
And then answer the questions.
11. QUAD is a _____________________.
12.
a = _______
13.
b = _______
14.
x = _______
15.
y = _______
U
a
b
A
x
53
y
Q
D
The perimeter of QUAD is 43.2 inches
and y is twice as long as x .
Q
a
16. QUAD (in this figure) is a _______________________.
17.
a = _______
18.
x = _______
19.
y = _______
23 feet
y
D
89
U
x
117
A
The perimeter of QUAD is 64 cm.
20. QUAD (in this figure) is a(n) ____________________________.
21.
a = _______
22.
w = _______
23.
x = _______
24.
y = _______
D
a
A
x
59
25.4 cm
w
Q
y
74
37 cm
U
IV. Show any work you feel necessary as you answer each of the following questions.
25. Find the sum of the measures of the interior angles in a convex polygon with 20 sides.
26.
If the convex polygon above is regular, what is the measure of one interior angle ?
27.
If an equiangular convex polygon has 32 sides, what is the measure of one exterior angle ?
28.
If the measure of one interior angle of a regular polygon is 156 degrees,
how many sides does the polygon have ?
29. In the figure to the right, only one
of the lengths of the segments
labeled x, y, and w can be found.
12.3 cm
14.8 cm
x
Find it and explain how and why it works.
14.9 cm
y
13.5 cm
w
13.5 cm
12.3 cm
30. Using the figure below, find the lengths of the lettered segments.
x = _______
14 in
f
y = _______
x
21 in
w = _______
y
w
f = _______
48 in
31. Using just the markings (not what your eyes are telling you), identify each of the following
quadrilaterals as either a rectangle, a rhombus, a parallelogram, a kite, a square,
or an isosceles trapezoid.
a.
d.
b.
e.
c.
f.
32.
Given :
RECT is a rectangle
Prove :
R
T
The diagonals are congruent
E
33.
TRAP below is a trapezoid.
C
MN is a midsegment of TRAP. RP and AT are diagonals.
If MC = 16 in and TP = 54 in find each of the following ...
R
CE = _______
A
RA = _______
M
C
T
E
N
MN = _______
P